Bounds for the rainbow connection number of graphs

• Autorzy: Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

An edge-coloured graph G is rainbow-connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow-connected. In this paper we show some new bounds for the rainbow connection number of graphs depending on the minimum degree and other graph parameters. Moreover, we discuss sharpness of some of these bounds.

Słowa kluczowe

EN

rainbow colouring; rainbow connectivity; extremal problem

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C35: Extremal problems

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2011
• Tom: 31
• Numer: 2
• Strony: 387-395

Daty

wydano

2011

otrzymano

2010-01-05

poprawiono

2011-01-14

zaakceptowano

2011-01-17

Twórcy

autor

Ingo Schiermeyer

• Institut für Diskrete Mathematik und Algebra, Technische Universität Bergakademie Freiberg, 09596 Freiberg Germany

Bibliografia

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• [7] A.B. Ericksen, A matter of security, Graduating Engineer & Computer Careers (2007) 24-28.
• [8] A. Kemnitz and I. Schiermeyer, Graphs with rainbow connection number two, Discuss. Math. Graph Theory 31 (2011) 313-320, doi: 10.7151/dmgt.1547.
• [9] M. Krivelevich and R. Yuster, The rainbow connection of a graph is (at most) reciprocal to its minimum degree, J. Graph Theory 63 (2010) 185-191.
• [10] V.B. Le and Z. Tuza, Finding optimal rainbow connection is hard, preprint 2009.
• [11] I. Schiermeyer, Rainbow connection in graphs with minimum degree three, International Workshop on Combinatorial Algorithms, IWOCA 2009, LNCS5874 (2009) 432-437.

Identyfikatory

DOI

10.7151/dmgt.1553